Considering uncertainty, awareness and ambiguity as a three-dimensional space

By Fabio Boschetti

Fabio Boschetti (biography)

The concept of unknown unknowns highlights the importance of introspection in assessing knowledge. It suggests that finding our way in the set of known-knowns, known-unknowns, unknown-knowns and unknown-unknowns, reduces to asking:

  1. how uncertain are we? and
  2. how aware are we of uncertainty?

When a problem involves a decision-making team, rather than a single individual, we also need to ask:

  1. how do context and perception affect what we know?

This third question pertains to ambiguity, understood as the extent to which framing a problem differently (reflecting different assumptions, priorities, values or morals) may lead to different conclusions. The distinction between uncertainty and ambiguity is significant: more information can reduce uncertainty but not ambiguity, since the latter may bias how this information is processed.

None of the above three questions has a black or white answer: in real world problems we are never fully certain or fully uncertain, fully aware or fully unaware; rather answers span a continuum. Uncertainty, awareness and ambiguity thus have the flavour of geometrical dimensions: they define an abstract 3 dimensional space where our state of knowledge can be mapped.

These insights can be turned to practical use by making introspection operational. We can monitor how, not just what, we think in relation to each of the three axes by using simple checklists. For example, to assess our level of uncertainty we may ask:

  • Where does my knowledge come from? Can I trust my sources?
  • Can I conceive counter-factuals, multiple scenarios, alternative system behaviours and outcomes?
  • How likely is it that my conclusion is correct?

To assess our awareness of uncertainty, we may ask:

  • Would I be able to describe my mental model of the problem to others?
  • And the underlying assumptions I use?
  • Have I chosen a mental model to fit the available evidence or my preferences?

When it comes to ambiguity:

  • Do I know my colleagues’ mental models?
  • How similar are they to mine? Is it likely that they are so similar as to prevent us from considering an alternative understanding? Is it likely that they are so dissimilar as to prevent us from reaching a shared understanding?
  • What are the assumptions underneath each team member’s reasoning?

And finally, the ultimate question which addresses all three axes:

  • What would change my mind? What evidence, novel insight or alternative framing would lead me to reconsider my conclusion?

The uncertainty-awareness-ambiguity three-dimensional space can also be used to monitor the process of knowledge production and how knowledge changes throughout the different phases of a project.

Of course, knowledge does not increase monotonically: the more we discover, the more our awareness of ignorance increases; the more parties we interact with, the more ambiguity is revealed. As a result, uncertainty and ambiguity may increase while our overall level of knowledge also increases, provided we are alert: awareness is key to realising that knowledge is more than the opposite of uncertainty.

For example, we normally assume that if we pick randomly from a deck of cards, the card is either red or black and thus the sum of their probability equals 1. But what if this was an unusual deck which also contained yellow cards? This potential unknown-unknown would make it possible for an outcome to be neither red nor black and thus the sum of the probabilities of red and black would be less than 1.

It would also mean that our statistical analysis was incomplete and we were overconfident of our predictive ability. The card picking problem now appears more complex and uncertain, but I would argue that our knowledge has increased since we better understand the set of configurations our system can display and, crucially, we are better prepared for them.

Within the uncertainty-awareness-ambiguity three-dimensional space, the traditional concept of unknown-unknown applies to the first two dimensions (uncertainty and awareness). Another type of unknown-unknown applies to the third dimension (ambiguity), when we do not know that a problem is ambiguous.

A stereotyped vignette provides an illustration: as an environmental scientist, I may believe I have enough scientific evidence to recommend conserving a specific natural resource. An economist colleague of mine may believe she has enough evidence to recommend exploiting the same natural resource. Unaware of each other’s knowledge or view, we may both have high confidence in our own recommendations.

However, as a team, my colleague and I are in a state of complete ambiguity since we cannot reach a joint recommendation until we bridge our disciplinary biases. The problem is now much more complex, as anyone working in natural resource management very well knows. However, once again, I argue that our combined level of knowledge has increased, because now we are aware that this gap exists and how it affects decision making.

The key suggestion here is that a richer consideration of unknown unknowns requires not only an outward search for more information and better system understanding, but also inward personal introspection on uncertainty and awareness of uncertainty and shared introspection on differences in perception and context (referred to here as ambiguity) among all of those involved in addressing a problem. The ultimate introspective effort lies not in asking ourselves to what extent our conclusions are correct, but to what extent they may be mistaken, leading us to explore what it would take “to change my mind.”

Do you find the uncertainty, awareness and ambiguity framework useful? Does it resonate with you? Do you have any experience with it? Do you have additional insights on this knowledge space? Do you have examples to share?

To find out more:
Boschetti F. (2011). A graphical representation of uncertainty in complex decision making. Emergence: Complexity and Organization, 13, 1 and 2: 146-168. (PDF 420KB)

This blog post is part of a series on unknown unknowns as part of a collaboration between the Australian National University and Defence Science and Technology.

For the 12 other blog posts already published in this series, see:

Biography: Fabio Boschetti PhD is a research scientist with CSIRO Oceans and Atmosphere in Crawley, Western Australia. He is an applied mathematician with strong multidisciplinary experience, which includes modelling physical, ecological and socio-economic processes. His current research focuses on better understanding the interaction between ecosystem functioning and human activities. For this he develops and employs different types of computational models, ranging from intermediate size models used to study complex multi-scale dynamics, to simpler models used to facilitate the communication of research results.

6 thoughts on “Considering uncertainty, awareness and ambiguity as a three-dimensional space”

  1. Thanks for such an interesting read.

    I especially like the idea of making a shared form of introspection on differences of perception and context operational to the point of changing minds. It resonates heavily with my work experience in transport and environmental planning. I have certainly encountered resistance to this form of introspection – some people feel comfortable, and even enthusiastic, about it; whereas some people are just not willing to go there….. I think the three-dimensional space idea would really help to tempt those who are generally more reluctant. Overall, that would then help to cultivate a more exploratory, flexible way of thinking and adaptation, rather than sticking safely (safe for whom?) with ‘the way we do things round here’ type of approach. Bridging disciplinary biases is such a huge challenge, meriting a great deal of attention over the years to come. Seeing this as a combined knowledge space to be expanded is very helpful indeed.

    • thanks Catherine, have you notice any pattern of resistance to introspection? maybe institutional, psychological, gender-based, age-based, discipline-based?

      • I would say that there were certain tendencies, based on my recollections of working across disciplines and attempting to achieve integrated action (beware non-scientific data alert!):
        – A tendency for females to be more open to self-criticism and introspection.
        – A tendency for senior people to find introspection easier when in a mixed gender group of peers (but not when subordinates are present).
        – A tendency for some senior people to prefer being wrong about something, as long as they sound certain; in preference to expressing uncertainty, which sounds like a weakness.
        – A tendency for those working in health and environmental planning to be more comfortable with introspection than those working in transport planning – that seemed to match with both an institutional and disciplinary culture (health agencies & local government; transport and environmental planning).
        – A tendency for age to be less relevant than perhaps may be expected – e.g. it’s not always the case that older, more experienced people are ‘set in their ways’ and new blood has to come in for a change to happen. Experience is actually a good partner for introspection, whether individual or shared. Mixing ages could be healthy if possible – whereas perhaps in research we tend to categorise research activity with certain age groups – young people, elderly people, middle-aged etc?

        People do seem very aware (almost too aware) of the risk of stepping on someone’s toes, or having their own toes stepped on – this means that people must feel comfortable and confident enough to talk about uncertainty, awareness and ambiguity without feeling threatened, or feeling that they are threatening others. If multidisciplinary working and being introspective was positioned to be more of a valued norm – without the associated threat(s) – this would hopefully lead to less ‘defence of the territory’ type of behaviour and be great for encouraging the much-needed rapid expansion of the combined knowledge space.

        • You wrote “A tendency for some senior people to prefer being wrong about something, as long as they sound certain”
          Sadly, the more an issue is uncertain and ambiguous, the more this behaviour is perversely ‘rational’. First, in most management problems, whether a view is right or wrong will be revealed in the future (if it all), while perception of uncertainty is immediate. Second, because of uncertainty and ambiguity, it may be impossible to certify a view as ‘wrong’, but it can be certified as uncertain.

          • Indeed, your two observations indicate that there are few (if any) negatives in terms of reputational risks for indulging in a false sense of certainty – the negatives instead accumulate through synthesis happening in the real world. Churchman (1967) has described taking a section of a wicked problem and finding a rational solution to this piece as taming the growl of the wicked problem: the wicked problem no longer shows its teeth before it bites.

            Yet maybe the only thing that is certain is uncertainty itself. This perhaps adds another paradox (certain uncertainty) to three which have been referred to by Ralph Stacey (stable instability, predictable unpredictability, regular irregularity) as a counterargument for a belief in certainty.

            Despite the patterns of resistance to introspection and engaging with uncertainty that we’ve discussed, I’m highly optimistic that more people are recognising the need to embrace complexity, uncertainty and ambiguity, more fully engaging in questioning and co-exploration by situating themselves in a transdisciplinary-present time-frame and questioning assumptions – changing minds and so on: something I have termed as the need for ‘synergistic vigilance’.

            Perhaps it’s the willing act of synergistic vigilance that is the gateway to your proposed realm of a three-dimensional space – uncomfortable for some – occupied by uncertainty, awareness and ambiguity that abound in real-world situations of complexity. The varied (disciplinary, institutional etc.) perceptions of such issues need to be aired, if not reconciled, in some way before it’s possible to move on constructively together.


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